MinT - Best Known (206−45, 206, s)-Nets in Base 3

Best Known (206−45, 206, s)-Nets in Base 3

(206−45, 206, 640)-Net over F₃ — Constructive and digital

Digital (161, 206, 640)-net over F₃, using

2 times m-reduction [i] based on digital (161, 208, 640)-net over F₃, using
- trace code for nets [i] based on digital (5, 52, 160)-net over F₈₁, using
  - net from sequence [i] based on digital (5, 159)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 5 and N(F) ≥ 160, using
      - a function field by SÃ©mirat [i]

(206−45, 206, 1500)-Net over F₃ — Digital

Digital (161, 206, 1500)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(206−45, 206, 126372)-Net in Base 3 — Upper bound on s

There is no (161, 206, 126373)-net in base 3, because

1 times m-reduction [i] would yield (161, 205, 126373)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 64 552501 068518 059925 605936 365878 205218 700901 356269 331504 745335 002458 088927 058747 299078 338835 788737 > 3²⁰⁵ [i]